Skip to main content
Log in

A nonlocal maximum likelihood estimation method for enhancing magnetic resonance phase maps

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

A phase map can be obtained from the real and imaginary components of a complex valued magnetic resonance (MR) image. Many applications, such as MR phase velocity mapping and susceptibility mapping, make use of the information contained in the MR phase maps. Unfortunately, noise in the complex MR signal affects the measurement of parameters related to phase (e.g, the phase velocity). In this paper, we propose a nonlocal maximum likelihood (NLML) estimation method for enhancing phase maps. The proposed method estimates the true underlying phase map from a noisy MR phase map. Experiments on both simulated and real data sets indicate that the proposed NLML method has a better performance in terms of qualitative and quantitative evaluations when compared to state-of-the-art methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Aja-Fernández, S., Alberola-López, C., Westin, C.: Noise and signal estimation in magnitude MRI and Rician distributed images: a LMMSE approach. IEEE Trans. Image Process. 17, 1383–1398 (2008)

    Article  MathSciNet  Google Scholar 

  2. Bioucas-Dias, J., Katkovnik, V., Astola, J., Egiazarian, K.: Absolute phase estimation: adaptive local denoising and global unwrapping. Appl. Opt. 47(29), 5358–5369 (2002)

    Article  Google Scholar 

  3. Bonny, J.M., Renou, J.P., Zanca, M.: Optimal measurement of magnitude and phase from MR data. J. Magn. Reson. Ser. B 113(2), 136–144 (1996)

    Article  Google Scholar 

  4. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4, 490–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chavez, S., Xiang, Q.S., An, L.: Understanding phase maps in MRI: a new cutline phase unwrapping method. IEEE Trans. Med. Imaging 21(8), 966–977 (2002)

    Article  Google Scholar 

  6. Cruz-EnrÃquez, H., Lorenzo-Ginori, J.: Combined wavelet and nonlinear filtering for MRI phase images. In: Kamel, M., Campilho, A. (eds.) Image Analysis and Recognition, Lecture Notes in Computer Science, vol. 5627, pp 83–92. Springer, Berlin (2009). iSBN: 978-3-642-02610-2

  7. den Dekker, A.J., Sijbers, J.: Data distributions in magnetic resonance images: a review. Phys. Med. 30(7), 725–741 (2014)

    Article  Google Scholar 

  8. Fisher, Y.: Pixelized Data. Springer, London (1995)

    Google Scholar 

  9. He, L., Greenshields, I.R.: A nonlocal maximum likelihood estimation method for Rician noise reduction in MR images. IEEE Trans. Med. Imaging 28, 165–172 (2009)

    Article  Google Scholar 

  10. Heydari, M., Karami, M.R., Babakhani, A.: A new adaptive coupled diffusion PDE for MRI Rician noise. Signal Image Video Process. 10(7), 1–8 (2016)

  11. ISMRM (2010) http://www.ismrm.org/mri_unbound/simulated.htm

  12. Krissian, K., Aja-Fernández, S.: Noise-driven anisotropic diffusion filtering of MRI. IEEE Trans. Image Process. 18(10), 2265–2274 (2009)

    Article  MathSciNet  Google Scholar 

  13. Lorenzo-Ginori, J.V., Plataniotis, K.N., Venetsanopoulos, A.N.: Nonlinear filtering for phase image denoising. IEEE Proc. Vis. Image Signal Process. 149(5), 290–296 (2002)

    Article  Google Scholar 

  14. Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: Mri denoising using non-local means. Med. Image Anal. 12(4), 514–523 (2008)

    Article  Google Scholar 

  15. Mohan, J., Krishnaveni, V., Guo, Y.: A survey on the magnetic resonance image denoising methods. Biomed. Signal Process. Control 9, 56–69 (2014)

    Article  Google Scholar 

  16. Rajan, J., Poot, D., Juntu, J., Sijbers, J.: Noise measurement from magnitude MRI using local estimates of variance and skewness. Phys. Med. Biol. 55, N441–N449 (2010)

    Article  Google Scholar 

  17. Rajan, J., Jeurissen, B., Verhoye, M., Van Audekerke, J., Sijbers, J.: Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods. Phys. Med. Biol. 56, 5221–5234 (2011)

    Article  Google Scholar 

  18. Rajan, J., Van Audekerke, J., Van der Linden, A., Verhoye, M., Sijbers, J.: An adaptive non local maximum likelihood estimation method for denoising magnetic resonance images. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), pp 1136–1139. IEEE (2012)

  19. Rajan, J., Veraart, J., Van Audekerke, J., Verhoye, M., Sijbers, J.: Nonlocal maximum likelihood estimation method for denoising multiple coil magnetic resonance images. Magn. Reson. Imaging 30(10), 1512–1518 (2012b)

    Article  Google Scholar 

  20. Rajan, J., den Dekker, A.J., Sijbers, J.: A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov–Smirnov test. Signal Proc. 103, 16–23 (2014)

  21. Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Automated unwrapping of MR phase images applied to BOLD MR venography at 3 Tesla. Magn. Reson. Imaging 18(2), 175–180 (2003)

    Article  Google Scholar 

  22. Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Magnetic susceptibility-weighted MR phase imaging of the human brain. J. Neuroradiol. 26(4), 736–742 (2005)

    Google Scholar 

  23. Riji, R., Rajan, J., Sijbers, J., Nair, M.S.: Iterative bilateral filter for Rician noise reduction in MR images. Signal Image Video Process. 9(7), 1543–1548 (2015)

    Article  Google Scholar 

  24. Sharif, M., Hussain, A., Jaffar, M.A., Choi, T.S.: Fuzzy-based hybrid filter for Rician noise removal. Signal Image and Video Process. 10(2), 215–224 (2016)

    Article  Google Scholar 

  25. Sijbers, J., den Dekker, A.J., Scheunders, P., Van Dyck, D.: Maximum likelihood estimation of Rician distribution parameters. IEEE Trans. Med. Imaging 17(3), 357–361 (1998)

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the Research Foundation-Flanders (FWO, Belgium) through project funding G037813N and the TOP BOF project University of Antwerp (TOP BOF project 26824).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to P. V. Sudeep.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sudeep, P.V., Palanisamy, P., Kesavadas, C. et al. A nonlocal maximum likelihood estimation method for enhancing magnetic resonance phase maps. SIViP 11, 913–920 (2017). https://doi.org/10.1007/s11760-016-1039-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-016-1039-6

Keywords

Navigation